Polytropic wind solutions via the Complex Plane Strategy

Solar-type stars generate spherical winds, which are pressure driven flows, that start subsonic, reach the sound speed at sonic point and transition to supersonic flows. The point, mathematically corresponds a singularity of system differential equations describing flow. In problem an isothermal wind, Parker solution provides exact analytical expression tuned appropriately so does not affect solution. However, if wind is polytropic it possible find numerical approach needs be followed. We study solutions winds by within gravitational field. pass smoothly from critical allow us impact changes index these winds. explore properties as function boundary conditions used. apply Complex Plane Strategy (CPS) we obtain numerically This allows avoid appearing in through introduction complex variables integration on plane. Applying this method, with physical behaviour stellar surface, large distances star. further role flow effect mass--loss rate temperature increase well decrease parameter both yield smoother velocity profile lower velocities shifts subsonic Finally, verify increasing coronal yields higher weaker dependence index.